In Truffula Land, a thneed is a popular manufactured textile produced by two firms: Swomee Industries and Barbaloot Suits, Inc. The thneeds produced by the firms are indistinguishable, and consumers will buy only from the firm with lower prices (demand will be split equally between the two firms if they set identical prices). Demand for thneeds is given by = 40 3. Where P is the lower of the prices charged by the two firms. Each firm incurs a constant unit cost of $5 per thneed produced. Initially, assume there are no capacity constraints on the production of either firm. (a) [10 points] The two firms engage in a one-shot price competition game. What prices will they set in a Nash equilibrium? What quantity of thneeds will be sold in Truffula Land? (b) [10 points] Truffula Land has strong enforcement of contracts, but it is a pre-antitrust society. Therefore, there is nothing stopping Swomee Industries and Barbaloot Suits from entering into a collusive contract. Suppose the two companies enter into a contract limiting their thneed production capacity. To keep things fair, suppose that they will each commit to the same capacity. What quantity limit should each commit to, in order to maximize their joint profits from thneed production? What price will prevail once they have these capacity commitments? (c) [6 points] Suppose that strong antitrust enforcement arrives in Truffula land, returning us to the setup of part (a). However, it is discovered that a by product of thneed production, gluppity-glup, has harmful environmental consequences. Researchers at Truffula University carefully quantify the economic impact of the gluppity-glup, and they determine that each thneed produced leads to $2 of cleanup costs (You make take for granted that the researchers got this number right). These costs are spread across the broader society; they are not incurred by the thneed producers themselves. Using a diagram, present the demand curve, private marginal cost (supply) curve, and social marginal cost curve. (d) [6 points] Explain conceptually how total surplus could be improved with government intervention in this case, and with what sort of policy. You may find it useful to add to or refer to your diagram from (c). (e) [8 points] Following up on (c) and (d), describe an optimal policy and compute how much it would improve total surplus.